Atomistic Molecular Dynamics Trajectories Research Articles

Simulation analysis of selective alanine mutation effect on stability of human prion protein

Prion diseases are neurodegenerative disorders caused by spongiform degeneration of the brain. Understanding the fundamental mechanism of prion protein aggregation caused by mutations is very crucial to resolve the pathology of prion diseases. To help understand the roles of individual residues on the stability of the human prion protein, the computational method of free energy simulations based on atomistic molecular dynamics trajectories is applied to Phe175 → Ala, Val180 → Ala, and Val209 → Ala mutations of the human prion protein. The simulations show that all three alanine mutations destabilize the human prion protein. The calculated free energy change differences, ΔΔG, for the Phe175 → Ala, Val180 → Ala, and Val209 → Ala mutations are in good agreement with the experimental values. The significant destabilizing effects on the mutants relative to the wild-type protein arise from van der Waals terms. Furthermore, our free energy decomposition analysis shows that the major contribution to destabilizing the V180A and V209A mutants relative to the wild-type protein is originated from van der Waals interactions from residues near the mutation sites. In contrast, the contribution to destabilizing the F175A mutant is mainly caused by van der Waals interactions from residues near and far away from the mutation site. Our results show that the free energy simulation with a thermodynamic integration approach for selected alanine scanning mutations is beneficial for understanding the detailed mechanism of human prion protein destabilization, specific residues' role, and the hydrophobic effect on protein stability. Communicated by Ramaswamy H. Sarma

Neural Upscaling from Residue-Level Protein Structure Networks to Atomistic Structures.

Coarse-graining is a powerful tool for extending the reach of dynamic models of proteins and other biological macromolecules. Topological coarse-graining, in which biomolecules or sets thereof are represented via graph structures, is a particularly useful way of obtaining highly compressed representations of molecular structures, and simulations operating via such representations can achieve substantial computational savings. A drawback of coarse-graining, however, is the loss of atomistic detail—an effect that is especially acute for topological representations such as protein structure networks (PSNs). Here, we introduce an approach based on a combination of machine learning and physically-guided refinement for inferring atomic coordinates from PSNs. This “neural upscaling” procedure exploits the constraints implied by PSNs on possible configurations, as well as differences in the likelihood of observing different configurations with the same PSN. Using a 1 μs atomistic molecular dynamics trajectory of A, we show that neural upscaling is able to effectively recapitulate detailed structural information for intrinsically disordered proteins, being particularly successful in recovering features such as transient secondary structure. These results suggest that scalable network-based models for protein structure and dynamics may be used in settings where atomistic detail is desired, with upscaling employed to impute atomic coordinates from PSNs.

Bayesian estimation of the hydroxyl radical diffusion coefficient at low temperature and high pressure from atomistic molecular dynamics.

The hydroxyl radical is the primary reactive oxygen species produced by the radiolysis of water and is a significant source of radiation damage to living organisms. Mobility of the hydroxyl radical at low temperatures and/or high pressures is hence a potentially important factor in determining the challenges facing psychrophilic and/or barophilic organisms in high-radiation environments (e.g., ice-interface or undersea environments in which radiative heating is a potential heat and energy source). Here, we estimate the diffusion coefficient for the hydroxyl radical in aqueous solution using a hierarchical Bayesian model based on atomistic molecular dynamics trajectories in TIP4P/2005 water over a range of temperatures and pressures.

Conservative Potentials for a Lattice-Mapped Coarse-Grained Scheme.

The conservative potential, arising from a coarse-grain (CG) mapping scheme for nonbonded atomistic particles, is studied. This is a bottom-up approach from first-principles that maps atomistic particles to fluid element-like subcells whose centers lie on a regular, cubic lattice. Unlike standard CG mapping schemes, the current one uses dynamic labeling which on-the-fly changes the CG labels of the particles. The subcells can also be different sizes and shapes, in principle. Equilibrium atomistic molecular dynamics trajectories for different Lennard-Jones fluids are calculated and converted to CG ones, from which CG probability distribution functions are calculated. Correlation studies show position and mass CG variables are uncoupled in a given subcell, as are different vector components of position. Furthermore, the strongest coupling occurs with neighboring cells in specific directions, and the resulting distribution is well described by a multivariate Gaussian. This implies the CG potential has a generalized quadratic form, whose derivative can be determined analytically. A microscopic rationalization is provided for the signs and relative magnitudes of different correlation coefficients, and in some cases, a connection is made with bulk properties of the fluid. We argue the generalized quadratic form should be robust to changes in the particulars of the CG scheme, as well as the nature of the atomistic intermolecular potential. Only a few potential parameters need to be calculated from the underlying atomistic system. This is significant because it indicates the transferability of this form to other, more complex systems. This transferability will be tested in future work, where mapping schemes with fuzzy boundaries will be considered.

Free energy simulations to understand the effect of Met → Ala mutations at positions 205, 206 and 213 on stability of human prion protein

Prion diseases are a family of infectious amyloid diseases affecting human and animals. Prion propagation in transmissible spongiform encephalopathies is associated with the unfolding and conversion of normal cellular prion protein into its pathogenic scrapie form. Understanding the fundamentals of prion protein aggregation caused by mutations is crucial to unravel the pathology of prion diseases. To help understand the contributions of individual residues to the stability of the human prion protein, we have carried out free energy simulations based on atomistic molecular dynamics trajectories. We focus on Met → Ala mutations at positions 205, 206 and 213, which are mostly buried residues located on helix 3 of the protein. The simulations predicted that all three mutations destabilize the prion protein. Changes in unfolding free energy upon mutation, ∆∆G, are 3.10 ± 0.79, 2.00 ± 0.26 and 3.06 ± 0.66 kcal/mol for M205A, M206A and M213A, respectively, in excellent agreement with the corresponding experimental values of 3.09 ± 0.28, 1.50 ± 0.34 and 3.12 ± 0.27 kcal/mol [T. Hart et al. (2009) PNAS 106, 5651–5656]. Component analysis indicates that the major contributions to the loss of protein stability arise from van der Waals interactions for the M205A and M206A mutations, and from van der Waals and covalent energy terms for M213A. Interestingly, while free energy contributions from a majority of residues neighboring the mutation sites tend to stabilize the wild type, there are a few residues stabilizing the mutant side chains. Our results show that this approach to free energy calculation can be very useful for understanding the detailed mechanism of human prion protein stability.

Bottom-Up Coarse-Grained Models for Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) have recently become a popular topic of study in the protein science community due to their role processes such as cellular signaling and liquid-liquid phase separation (LLPS). A number of coarse-grained models for IDPs have been recently been developed. These models are typically of the top-down variety; they are parameterized to reproduce a set of experimental information. While these models have been effective for providing a computational basis for the study processes such as LLPS, they must rely on assumptions about the interactions between coarse-grained sites due to the lack of microscopic information. This is contrasted with bottom-up coarse-graining, which relies on data from a higher resolution source, like an atomistic molecular dynamics trajectory, to parameterize the model. Using high-quality atomistic data generated from recently developed force-fields, we have developed multiscale coarse-grained and relative entropy minimization coarse-grained models of several residues common among IDPs. These models are not limited to the standard Lennard-Jones and screened electrostatic functional forms typically used in top-down coarse-grained models. This model is also able to better capture the effects of solvation on the IDP. These new functional forms provide a basis to create a full interaction matrix that is based on mixing rules determined for a small number of residues. This new model creates higher fidelity coarse-grained model for the study LLPS as well as providing a basis-set for parameterizing interactions of new top-down models.

Combining Molecular and Spin Dynamics Simulations with Solid-State NMR: A Case Study of Amphiphilic Lysine-Leucine Repeat Peptide Aggregates.

Interpreting dynamics in solid-state molecular systems requires characterization of the potentially heterogeneous environmental contexts of molecules. In particular, the analysis of solid-state nuclear magnetic resonance (ssNMR) data to elucidate molecular dynamics (MD) involves modeling the restriction to overall tumbling by neighbors, as well as the concentrations of water and buffer. In this exploration of the factors that influence motion, we utilize atomistic MD trajectories of peptide aggregates with varying hydration to mimic an amorphous solid-state environment and predict ssNMR relaxation rates. We also account for spin diffusion in multiply spin-labeled (up to 19 nuclei) residues, with several models of dipolar-coupling networks. The framework serves as a general approach to determine essential spin couplings affecting relaxation, benchmark MD force fields, and reveal the hydration dependence of dynamics in a crowded environment. We demonstrate the methodology on a previously characterized amphiphilic 14-residue lysine-leucine repeat peptide, LKα14 (Ac-LKKLLKLLKKLLKL-c), which has an α-helical secondary structure and putatively forms leucine-burying tetramers in the solid state. We measure the R1 relaxation rates of uniformly 13C-labeled and site-specific 2H-labeled leucines in the hydrophobic core of LKα14 at multiple hydration levels. Studies of 9 and 18 tetramer bundles reveal the following: (a) for the incoherent component of 13C relaxation, the nearest-neighbor spin interactions dominate, while the 1H-1H interactions have minimal impact; (b) the AMBER ff14SB dihedral barriers for the leucine Cγ-Cδ bond ("methyl rotation barriers") must be lowered by a factor of 0.7 to better match the 2H data; (c) proton-driven spin diffusion explains some of the discrepancy between experimental and simulated rates for the Cβ and Cα nuclei; and (d) 13C relaxation rates are mostly underestimated in the MD simulations at all hydrations, and the discrepancies identify likely motions missing in the 50 ns MD trajectories.

Molecular modeling and simulation of atactic polystyrene/amorphous silica nanocomposites

The local structure, segmental dynamics, topological analysis of entanglement networks and mechanical properties of atactic polystyrene - amorphous silica nanocomposites are studied via molecular simulations using two interconnected levels of representation: (a) A coarse - grained level. Equilibration at all length scales at this level is achieved via connectivity - altering Monte Carlo simulations. (b) An atomistic level. Initial configurations for atomistic Molecular Dynamics (MD) simulations are obtained by reverse mapping well- equilibrated coarse-grained configurations. By analyzing atomistic MD trajectories, the polymer density profile is found to exhibit layering in the vicinity of the nanoparticle surface. The dynamics of polystyrene (in neat and filled melt systems) is characterized in terms of bond orientation. Well-equilibrated coarse-grained long-chain configurations are reduced to entanglement networks via topological analysis with the CReTA algorithm. Atomistic simulation results for the mechanical properties are compared to the experimental measurements and other computational works.

Thermal and mechanical properties of thermosetting polymers using coarse-grained simulation

We developed coarse-grained (CG) molecular representations of mixtures of diglycidyl ether of bisphenol-A (DGEBA) and poly(oxypropylene) diamine (POP-DA) for use in CG molecular dynamics (MD) simulations. In the CG representation, DGEBA is comprised of three beads of two types and POP-DA also by three beads of two types. Atomistic MD of liquid systems was performed to derive intra- and inter-bead potentials via Boltzmann inversion. While the bonded potentials, composed of bond stretching and angle bending, were parameterized directly from the distribution functions of all atomistic molecular dynamics trajectories, the non-bonded potentials were derived from the iterative Boltzmann Inversion with a given set of coarse-grained interactions. CG systems correctly reproduced liquid and crosslinked densities. Under uniaxial tension, the Young's modulus of the CG systems was much lower than the experimental value, and we show this arises from the assumed form of the extrapolated regions of the CG potentials. By stiffening these regions, we increased the CG Young's modulus of the crosslinked systems without sacrificing the correct prediction of density. This suggests that transferrable CG potentials can be optimized for use in non-equilibrium MD for property estimation.

Simulation of Multi-Dimensional Signals in the Optical Domain: Quantum-Classical Feedback in Nonlinear Exciton Propagation.

We present an algorithm for the simulation of nonlinear 2D spectra of molecular systems in the UV-vis spectral region from atomistic molecular dynamics trajectories subject to nonadiabatic relaxation. We combine the nonlinear exciton propagation (NEP) protocol, that relies on a quasiparticle approach with the surface hopping methodology to account for quantum-classical feedback during the dynamics. Phenomena, such as dynamic Stokes shift due to nuclear relaxation, spectral diffusion, and population transfer among electronic states, are thus naturally included and benchmarked on a model of two electronic states coupled to a harmonic coordinate and a classical heatbath. The capabilities of the algorithm are further demonstrated for the bichromophore diphenylmethane that is described in a fully microscopic fashion including all 69 classical nuclear degrees of freedom. We demonstrate that simulated 2D signals are especially sensitive to the applied theoretical approximations (i.e., choice of active space in the CASSCF method) where population dynamics appears comparable.

Fluctuating Finite Element Analysis: Development and Applications to Cytoplasmic Dynein

The number of structures in the Electron Microscopy Database (EMDB) is growing rapidly due to improvements in cryo-electron microscopy and tomography [1]. This database is complementary to the Protein Data Base (PDB), in that it contains volumetric information about the overall shape of a biomolecule, rather than fully atomistic structures. Fluctuating Finite Element Analysis (FFEA) [2] is a new computer simulation technique that simulates the dynamic behaviour of bio-molecular structures in the EMDB, in an analogous manner to the use of atomistic molecular dynamics trajectories based on structures deposited in the PDB. As FFEA uses a continuum representation of biomolecules it has no upper length-scale limit, and provides access to mesoscopic regimes (50-1000nm) inaccessible to more detailed modelling techniques.To model the action of molecular motors using FFEA, we account for atomistic processes such as ATP binding, hydrolysis and changes in protein secondary structure by including them as instantaneous events occurring at a given rate. Coupling the temperature driven dynamics of the motor with the probability that a transition will occur ensures that the internal strain energy influences the rate of the chemical processes driving the action of the motor. We are currently applying this coupled simulation to cytoplasmic dynein, which is a dimeric molecular motor involved in intracellular cargo transport, to study how mechanical communication and gating between the two subunits enables the motor to walk without moving backwards, stalling or releasing from the microtubule completely.[1] Kuehlbrandt, W., The Resolution Revolution, Science. 2014, 343(6178), 1443-4.[2] Oliver, R. C., Read, D. J., Harlen, O. G. And Harris, S. A., A stochastic finite element model for the dynamics of globular macromolecules, J. Comp. Phys. 2013, 239, 147-65.

Molecular structure and elastic properties of thermotropic liquid crystals: Integrated molecular dynamics—Statistical mechanical theory vs molecular field approach

The connection between the molecular structure of liquid crystals and their elastic properties, which control the director deformations relevant for electro-optic applications, remains a challenging objective for theories and computations. Here, we compare two methods that have been proposed to this purpose, both characterized by a detailed molecular level description. One is an integrated molecular dynamics-statistical mechanical approach, where the bulk elastic constants of nematics are calculated from the direct correlation function (DCFs) and the single molecule orientational distribution function [D. A. McQuarrie, Statistical Mechanics (Harper & Row, New York, 1973)]. The latter is obtained from atomistic molecular dynamics trajectories, together with the radial distribution function, from which the DCF is then determined by solving the Ornstein-Zernike equation. The other approach is based on a molecular field theory, where the potential of mean torque experienced by a mesogen in the liquid crystal phase is parameterized according to its molecular surface. In this case, the calculation of elastic constants is combined with the Monte Carlo sampling of single molecule conformations. Using these different approaches, but the same description, at the level of molecular geometry and torsional potentials, we have investigated the elastic properties of the nematic phase of two typical mesogens, 4'-n-pentyloxy-4-cyanobiphenyl and 4'-n-heptyloxy-4-cyanobiphenyl. Both methods yield K3(bend) >K1 (splay) >K2 (twist), although there are some discrepancies in the average elastic constants and in their anisotropy. These are interpreted in terms of the different approximations and the different ways of accounting for the structural properties of molecules in the two approaches. In general, the results point to the role of the molecular shape, which is modulated by the conformational freedom and cannot be fully accounted for by a single descriptor such as the aspect ratio.

Conformational dynamics of human IAPP monomers

We study the conformational dynamics of the human Islet Amyloid Polypeptide (hIAPP) molecule – a 37 residue-long peptide associated to type 2 diabetes – using molecular dynamics (MD) simulations. We identify partially structured conformational states of the hIAPP monomer, categorized by both end-to-end distance and secondary structure, as suggested by previous experimental and computational studies. The MD trajectories of hIAPP are analyzed using data-driven methods, in particular principal component analysis, in order to identify preferred conformational states of the amylin monomer and to discuss their relative stability as compared to corresponding states in the amylin dimer. These potential hIAPP conformational states could be further tested and described experimentally, or in conjunction with modern computational analysis tools such as Markov state-based methods for extracting kinetics and thermodynamics from atomistic MD trajectories.

The multiscale coarse-graining method. VII. Free energy decomposition of coarse-grained effective potentials

The potential of mean force (PMF) with respect to coarse-grained (CG) coordinates is often calculated in order to study the molecular interactions in atomistic molecular dynamics (MD) simulations. The multiscale coarse-graining (MS-CG) approach enables the computation of the many-body PMF of an atomistic system in terms of the CG coordinates, which can be used to parameterize CG models based on all-atom configurations. We demonstrate here that the MS-CG method can also be used to analyze the CG interactions from atomistic MD trajectories via PMF calculations. In addition, MS-CG calculations at different temperatures are performed to decompose the PMF values into energetic and entropic contributions as a function of the CG coordinates, which provides more thermodynamic information regarding the atomistic system. Two numerical examples, liquid methanol and a dimyristoylphosphatidylcholine lipid bilayer, are presented. The results show that MS-CG can be used as an analysis tool, comparable to various free energy computation methods. The differences between the MS-CG approach and other PMF calculation methods, as well as the characteristics and advantages of MS-CG, are also discussed.

Dynamic coupling between the LID and NMP domain motions in the catalytic conversion of ATP and AMP to ADP by adenylate kinase

The catalytic conversion of adenosine triphosphate (ATP) and adenosine monophosphate (AMP) to adenosine diphosphate (ADP) by adenylate kinase (ADK) involves large amplitude, ligand induced domain motions, involving the opening and the closing of ATP binding domain (LID) and AMP binding domain (NMP) domains, during the repeated catalytic cycle. We discover and analyze an interesting dynamical coupling between the motion of the two domains during the opening, using large scale atomistic molecular dynamics trajectory analysis, covariance analysis, and multidimensional free energy calculations with explicit water. Initially, the LID domain must open by a certain amount before the NMP domain can begin to open. Dynamical correlation map shows interesting cross-peak between LID and NMP domain which suggests the presence of correlated motion between them. This is also reflected in our calculated two-dimensional free energy surface contour diagram which has an interesting elliptic shape, revealing a strong correlation between the opening of the LID domain and that of the NMP domain. Our free energy surface of the LID domain motion is rugged due to interaction with water and the signature of ruggedness is evident in the observed root mean square deviation variation and its fluctuation time correlation functions. We develop a correlated dynamical disorder-type theoretical model to explain the observed dynamic coupling between the motion of the two domains in ADK. Our model correctly reproduces several features of the cross-correlation observed in simulations.

MoDEL (Molecular Dynamics Extended Library): A Database of Atomistic Molecular Dynamics Trajectories

More than 1700 trajectories of proteins representative of monomeric soluble structures in the protein data bank (PDB) have been obtained by means of state-of-the-art atomistic molecular dynamics simulations in near-physiological conditions. The trajectories and analyses are stored in a large data warehouse, which can be queried for dynamic information on proteins, including interactions. Here, we describe the project and the structure and contents of our database, and provide examples of how it can be used to describe the global flexibility properties of proteins. Basic analyses and trajectories stripped of solvent molecules at a reduced resolution level are available from our web server.

Approaching Elastic Network Models to Molecular Dynamics Flexibility.

Elastic network models (ENMs) are coarse-grained descriptions of proteins as networks of coupled harmonic oscillators. However, despite their widespread application to study collective movements, there is still no consensus parametrization for the ENMs. When compared to molecular dynamics (MD) flexibility in solution, the ENMs tend to disperse the important motions into multiple modes. We present here a new ENM, trained against a database of atomistic MD trajectories. The role of residue connectivity, the analytical form of the force constants, and the threshold for interactions were systematically explored. We found that contacts between the three nearest sequence neighbors are crucial determinants of the fundamental motions. We developed a new general potential function including both the sequential and spatial relationships between interacting residue pairs which is robust against size and fold variations. The proposed model provides a systematic improvement compared to standard ENMs: Not only do its results match the MD results-even for long time scales-but also the model is able to capture large X-ray conformational transitions as well as NMR ensemble diversity.

REACH: A program for coarse-grained biomolecular simulation

REACH ( Realistic Extension Algorithm via Covariance Hessian) is a program package for residue-scale coarse-grained biomolecular simulation. The program calculates the force constants of a residue-scale elastic network model in single-domain proteins using the variance–covariance matrix obtained from atomistic molecular dynamics simulation. Secondary-structure dependence of the force constants is integrated. The method involves self-consistent, direct mapping of atomistic simulation results onto a coarse-grained force field in an efficient automated procedure without requiring iterative fits and avoiding system dependence. Program summary Program title: REACH Catalogue identifier: AEDA_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEDA_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 42 244 No. of bytes in distributed program, including test data, etc.: 3 682 118 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: x86 PC Operating system: GNU/Linux, SUSE and Red Hat RAM: Depends on the system size to be calculated Word size: 32 or 64 bits Classification: 3 External routines: LAPACK, BLAS Nature of problem: A direct calculation of force field for residue-scale coarse-grained biomolecular simulation derived from atomistic molecular dynamics trajectory. Solution method: A variance–covariance matrix and the associated Hessian (second-derivative) matrix are calculated from an atomistic molecular dynamics trajectory of single-domain protein internal motion and the off-diagonal Hessian matrix is fitted to that of a residue-scale elastic network model. The resulting force constants for the residue pair interactions are expressed as model functions as a function of pairwise distance. Running time: Depends on the system size and the number of MD trajectory frames used. The test run provided with the distribution takes only a few seconds to execute.

A Systematic Methodology for Defining Coarse-Grained Sites in Large Biomolecules

Coarse-grained (CG) models of biomolecules have recently attracted considerable interest because they enable the simulation of complex biological systems on length-scales and timescales that are inaccessible for atomistic molecular dynamics simulation. A CG model is defined by a map that transforms an atomically detailed configuration into a CG configuration. For CG models of relatively small biomolecules or in cases that the CG and all-atom models have similar resolution, the construction of this map is relatively straightforward and can be guided by chemical intuition. However, it is more challenging to construct a CG map when large and complex domains of biomolecules have to be represented by relatively few CG sites. This work introduces a new and systematic methodology called essential dynamics coarse-graining (ED-CG). This approach constructs a CG map of the primary sequence at a chosen resolution for an arbitrarily complex biomolecule. In particular, the resulting ED-CG method variationally determines the CG sites that reflect the essential dynamics characterized by principal component analysis of an atomistic molecular dynamics trajectory. Numerical calculations illustrate this approach for the HIV-1 CA protein dimer and ATP-bound G-actin. Importantly, since the CG sites are constructed from the primary sequence of the biomolecule, the resulting ED-CG model may be better suited to appropriately explore protein conformational space than those from other CG methods at the same degree of resolution.

Coarse-Grained Biomolecular Simulation with REACH: Realistic Extension Algorithm via Covariance Hessian

Coarse-graining of protein interactions provides a means of simulating large biological systems. Here, a coarse-graining method, REACH, is introduced, in which the force constants of a residue-scale elastic network model are calculated from the variance-covariance matrix obtained from atomistic molecular dynamics (MD) simulation. In test calculations, the C α -atoms variance-covariance matrices are calculated from the ensembles of 1-ns atomistic MD trajectories in monomeric and dimeric myoglobin, and used to derive coarse-grained force constants for the local and nonbonded interactions. Construction of analytical model functions of the distance-dependence of the interresidue force constants allows rapid calculation of the REACH normal modes. The model force constants from monomeric and dimeric myoglobin are found to be similar in magnitude to each other. The MD intra- and intermolecular mean-square fluctuations and the vibrational density of states are well reproduced by the residue-scale REACH normal modes without requiring rescaling of the force constant parameters. The temperature-dependence of the myoglobin REACH force constants reveals that the dynamical transition in protein internal fluctuations arises principally from softening of the elasticity in the nonlocal interactions. The REACH method is found to be a reliable way of determining spatiotemporal protein motion without the need for expensive computations of long atomistic MD simulations.